You have twelve coins. You know that one is fake. The only thing that distinguishes the fake from the real ones is that its weight is slightly different. You have a balance scale that only tells you whether or not both sides are even. Find a method to determine which coin is fake and whether it is heavier or lighter than a real one using the scale only three times.

Use only the twelve coins themselves and no others, no other weights, no cutting coins, no pencil marks on the scale... etc.